Abstract
Nonnegative matrix factorization-based image representation algorithms have been widely applied to deal with high-dimensional data in the past few years. In this paper, we propose a graph regularized constrained nonnegative matrix factorization with L p Smoothing (GCNMFS) for image representation. Specifically, the main contributions of the proposed GCNMFS method include as follows: firstly, the geometric manifold structure hidden in data is effectively exploited by adopting a graph regularizer. Secondly, the label information of labeled samples is incorporated into the model of NMF without additional parameters. Finally, the L p smoothness constraint is used to constrain the basis matrix, and thus a smooth and more accurate solution is produced. Moreover, an effective optimization scheme is presented to solve the proposed model. Extensive experiments on several image datasets show the proposed GCNMFS method can achieve better performance than other state-of-the-art methods in clustering.
Highlights
Data representation has received considerable attention in practice for many years
FUNCTION OF GSNMFS To make full use of the prior knowledge, in this paper, we propose the GCNMFS method to deal with high-dimensional data
It can be observed that our proposed GCNMFS method is superior to other competitors, mainly because it takes advantage of the most prior knowledge of data, such as label information, manifold structure information and smoothness of solution, compared with other methods in clustering
Summary
Data representation has received considerable attention in practice for many years. Many popular data representation methods, such as principal component analysis (PCA) [1], linear discriminant analysis (LDA) [2], independent component analysis (ICA) [3], singular value decomposition (SVD), [4] non-negative matrix factorization (NMF) [5], [6] and concept factorization (CF) [7], have been used to solve many problems in the real world. Z. Shu et al.: Graph Regularized Constrained NMF With Lp Smoothness for Image Representation manifold structure of data. Sun et al [22] proposed a sparse dual graph regularized NMF method that takes advantage of the dual manifold structure and the sparseness of the coefficient matrix. Sun et al [24] proposed a graph regularized and sparse nonnegative matrix factorization with hard constraints method. Many studies have shown that the smoothness assumption plays an important role in data representation [25]–[29] To solve this issue, Leng et al [28] proposed to constrain the basis matrix with the Lp smoothing. We propose a novel method, called graph regularized constrained nonnegative matrix factorization with Lp smoothing (GCNMFS), for data representation.
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